Finite Group DatabasebetaFinite Group Databasebeta| order | 10164 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D33⋊D77 |
| Fitting, socle, derived, Hall | C3×C7×C112 ⋊ C22 |
| Hall | C7×C112 ⋊ C2×D3 |
| Hall | C3×C112 ⋊ C2×D7 |
| Sylow | C112 ⋊ D3×D7 |
| Hall | C3×C7 ⋊ D112 |
| Sylow | C7 ⋊ D33⋊D11 |
| Sylow | C3 ⋊ D11×D77 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C112 | C22 |
| LCS | G ▷ C3×C7×C112 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,7,11^2|d^a=d^6,e^a=e^10,f^a=f^10,c^b=c^2,f^b=f^10705 conjugacy classes — view the full character table.
| maximal subgroup of | #14546095⋊D7, D99⋊D77, D33⋊(C11⋊AGL(1,𝔽7)), … |
| maximal normal subgroup of | D33⋊(C11⋊AGL(1,𝔽7)), C3×D33⋊D77 |
| maximal quotient of | D99⋊D77, C3×D33⋊D77, D33⋊D231, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10164, 122);